Unbounded Reinhardt domains with finite-dimensional Bergman spaces in $\C^n$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917277558898688 |
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| author | Hayashida, Chika Kamimoto, Joe |
| author_facet | Hayashida, Chika Kamimoto, Joe |
| contents | In this paper, we construct unbounded domains in $\C^n$ ($n\geq 2$), whose Bergman spaces are nontrivial and finite-dimensional. We further show that the Bergman metrics on these domains have positive constant sectional curvature equal to $2$, and that their holomorphic automorphism groups consist only of linear mappings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unbounded Reinhardt domains with finite-dimensional Bergman spaces in $\C^n$ Hayashida, Chika Kamimoto, Joe Complex Variables 32A36 (32A40, 53C55, 32M05) In this paper, we construct unbounded domains in $\C^n$ ($n\geq 2$), whose Bergman spaces are nontrivial and finite-dimensional. We further show that the Bergman metrics on these domains have positive constant sectional curvature equal to $2$, and that their holomorphic automorphism groups consist only of linear mappings. |
| title | Unbounded Reinhardt domains with finite-dimensional Bergman spaces in $\C^n$ |
| topic | Complex Variables 32A36 (32A40, 53C55, 32M05) |
| url | https://arxiv.org/abs/2602.13732 |